面向未知杂乱环境中机器人导航的几何感知安全关键型局部反应控制器
Geometry-Aware Safety-Critical Local Reactive Controller for Robot Navigation in Unknown and Cluttered Environments
AI总结：
本研究针对未知杂乱环境下机器人导航问题，提出基于多项式优化与SOS近似的几何感知安全关键型局部反应控制器，通过凸化为SDP实现实时求解，验证了其安全性与跟踪性能优势。
摘要：
本研究提出一种安全关键型局部反应控制器，可实现机器人在未知杂乱环境中的导航。具体而言，轨迹跟踪任务被构建为一个带约束的多项式优化问题。随后，结合多项式正性证书概念及其Sum-of-Squares（SOS，平方和）近似，对控制变量施加安全约束，从而将机器人运动限制在局部提取的凸自由区域内。值得注意的是，在设计所提安全约束的过程中，机器人的几何外形可采用任何能用一组多项式函数表征的形状进行近似。该优化问题进一步利用截断多序列（tms）和矩松弛被凸化为半定规划（SDP），这十分有利于有效使用现成的锥规划求解器，从而可实现实时性能。我们开展了多种机器人导航任务研究，以验证所提方法在安全性和跟踪性能方面的有效性。
英文摘要：
This work proposes a safety-critical local reactive controller that enables the robot to navigate in unknown and cluttered environments. In particular, the trajectory tracking task is formulated as a constrained polynomial optimization problem. Then, safety constraints are imposed on the control variables invoking the notion of polynomial positivity certificates in conjunction with their Sum-of-Squares (SOS) approximation, thereby confining the robot motion inside the locally extracted convex free region. It is noteworthy that, in the process of devising the proposed safety constraints, the geometry of the robot can be approximated using any shape that can be characterized with a set of polynomial functions. The optimization problem is further convexified into a semidefinite program (SDP) leveraging truncated multi-sequences (tms) and moment relaxation, which favorably facilitates the effective use of off-the-shelf conic programming solvers, such that real-time performance is attainable. Various robot navigation tasks are investigated to demonstrate the effectiveness of the proposed approach in terms of safety and tracking performance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
